Supplementing Pascal

Pascal's wager is an unappreciated intellectual gem. It was posthumously published and it follows that Pascal was never able to directly respond to his critics. Nonsense criticisms have been presented and the absence of defense has been mistaken by some as Pascal's defeat. The truth is that the criticisms are so mundane it's hard for a serious thinker to see value in refuting them. Like the nonsense which crops up in the comments section of a YouTube video. Entertaining the nonsense, I previously presented a trivial defense and extension of the wager which I call the Vandivierian Wager. The topic recently came up in class and in a lively Facebook discussion, so I am adding some supplementary notes. Here is a thumbnail of the Vandivierian Wager:

1. Suppose each candidate system has a unique cost of salvation and positive infinite return, conditional on salvation.
2. Suppose Christianity is the candidate belief system with 0 cost of salvation.
   1. Due to Christianity's unique doctrine of Salvation by Faith Alone
3. Suppose an individual should select to maximize ROI.
4. From 2 and 3, Christianity obtains maximal ROI.
5. From 3 and 4, and individual should adopt Christianity.

Some objections raised:

1. What about the probability of the infinite number of ad hoc religious fictions which might be imagined?
2. Isn't the subtraction of infinites fallacious?
   1. Couldn't the cost be an infinite set as well?
3. How is it that you can call Christianity a credible or plausible belief system?

Ad Hoc Religion The Vandivierian Wager improves on Pascal's Wager in part by introducing a belief system filter. The filter solves the many gods problem among others by identifying a finite number of candidate belief systems according to some criteria. The original filter was a minimalist version which is easily made stronger by adopting additional assumptions or requirements. In the original version of the filter, the criteria were that:

1. The religion must actually exist.
2. The religion must yield positive infinite utility.

Why are these valid criteria for such a filter?

1. The religion must actually exist.
   1. No individual ever takes a gamble in the absence of knowledge about its existence.
   2. Existence is a minimalist credibility check. This is in part because it is a proxy for durability or sustainability and truth is durable. Further checks are encouraged, and will be discussed later on.
   3. If we did not impose this restriction then we would welcome an infinite list of fictions. Such a list is not open to exhaustive or concrete comparative analysis. This is a related but separate reason compared to 1.2, which would further add that such fictions have no expected truth in them anyway.
2. The religion must yield positive infinite utility.
   1. Given that some religions with positive infinite utility and finite cost exist, any religion which lacks positive infinite utility is a comparatively bad investment.
   2. Some religions, those which often pass this test, identify an eternal reward for salvation. Eternity is infinite in length, and a first-pass assumption about utility in each period is that each period obtains 1 unit of utility. This would lead to the smallest kind of infinity, as described by Cantor, equal to the cardinality of the set of natural numbers.
      1. Note that to calculate the total benefit, we don't care about set cardinality. Instead, we care about the comparative total area under the curve.
      2. However, if we obtain utility of 1 in each period then the integral is equal to the cardinality.
      3. I'm open to arguments that the perpetual utility of two different concepts of salvation are not equal (eg Christian Heaven sounds way more fun than Buddhist Nirvana), but for the sake of simplicity that is exempted from the current version of the argument. There is no reason to think utility from salvation converges, so we would ostensibly need to compare divergence rates in that case.

Subtracting Infinities What Makes Christianity (or Any Other Religion) Credible?The Vandivierian Wager should be taken as a drop in the apologetical ocean, not a stand-alone proof of any sort. Other logical arguments and empirical facts serve to validate the Bible as scripture and the doctrine of Christianity, properly understood, as true: -The Ontological Argument in particular (what would be better than if God were rational to believe in? If God actually existed! God is perfect, existence is a quality of perfection, therefore God exists.) Candidate religions:

1. Are real, not ad hoc
2. Have heterogeneous credibility / expected probability of truth
3. Have heterogeneous costs of salvation
4. Have positive infinite rewards

One may argue that 'Christianity rightly understood' is a moving target, and I absolutely agree. I support a 'two books' understanding of religion: Our worldview should inform our science and our science should interact with our interpretation of scripture. In the same way that we continually discover new scientific realities, I believe we should continually seek to improve our exegesis and our interpersonal relationships with God and the Church. These notes seem obvious to me, but on reflection it should be obvious that they aren't obvious to everyone. I think a serious case can be made that weak atheism is a case of rational ignorance. The opportunity cost of religious search, bolstered by the bore of religion, the predominance of incorrect religion, and the predominance of the ignorant even within the true religion of Christianity, along with other factors including a distaste for the possibility of objective moral rules, contribute to a cost benefit result in favor of rational ignorance for many individuals. Some other time I might write more on that as it leaves uncovered quite a bit.